The aurora borealis, which is more difficult to understand, and which necessitates more extended scientific notions, has remained much longer unexplained. This enigmatic phenomenon was especially striking to the imagination of ancient peoples. It was regarded as an omen of inauspicious events, and the historians who describe it affirm that, at times, armies have been seen passing through the bloody heavens, and that the clash of arms has been heard. It is now known that the aurora borealis has the same origin as lightning, that it is one of the visible manifestations of atmospheric electricity, and that it is due to slow movements of that fluid, while lightning is the result of violent motions. The effects of the aurora and of the thunderbolt are absolutely different; but between them there is an intermediary that connects them, and this is heat lightning. These elementary notions are now the property of science; but the study of the aurora has hitherto been only partially outlined. Travelers and physicists have, indeed, given numerous descriptions, but it has remained to find the bonds that unite these so important phenomena in the economy of the globe, to study the causes that set them in action, to observe the correlations that they may offer, and to discuss theories. This is a labor that Mr. S. Lemstrom has been engaged in for several years, and we now propose to analyze the results published by this great Finnish physicist. The author of this important work, who has long been occupied in the study of the aurora borealis, so frequent in his country, was attached to the polar expedition made in 1868 by Nordenskjold. He was led to begin a series of important observations. In 1871 he visited Finnish Lapland, and, after a series of ingenious researches, constructed an apparatus that permitted him to artificially reproduce the light of the aurora, and to present science with a summary of new and incontestable facts. Mr. Lemstrom has observed a large number of auroræ, and before touching upon theoretic questions, we shall give his description of one of the phenomena that seems to him to be the completest. On the 18th of October, 1868, the steamer Sophia was nearing the coast of Norway, after battling with a furious sea for three days in succession.